Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C43 ⋊ #1951 |
196 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|a^2=f,b^2=f,c^2=e,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dg,h^b=h^42,h^c=h^42494 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1951, C2×#19135374, #25100147, … |
| maximal normal subgroup of | D43×#1951, C2×#19135374, #25100147, … |
| maximal quotient of | #24995207, #24995217, #24995227, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 5289);